

class        A__:
						"""simple docstring"""






						def __init__(    self  ,      _lowercase = ""  ,      _lowercase = False    )     -> None:
									# Mapping from the first character of the prefix of the node
									a_						:						dict[str, RadixNode] 							= {}

									# A node will be a leaf if the tree contains its word
									a_						:						Any 							= is_leaf

									a_						:						str 							= prefix





						def 			UpperCamelCase__					(    self  ,      _lowercase    )     -> tuple[str, str, str]:
									a_						:						Optional[Any] 							= 0
									for q, w in zip(self.prefix  ,      _lowercase    ):
												if q != w:
															break

												x += 1

									return self.prefix[:x], self.prefix[x:], word[x:]





						def 			UpperCamelCase__					(    self  ,      _lowercase    )     -> None:
									for word in words:
												self.insert(_lowercase    )





						def 			UpperCamelCase__					(    self  ,      _lowercase    )     -> None:
									# Case 1: If the word is the prefix of the node
									# Solution: We set the current node as leaf
									if self.prefix == word:
												a_						:						List[Any] 							= True

									# Case 2: The node has no edges that have a prefix to the word
									# Solution: We create an edge from the current node to a new one
									# containing the word
									elif word[0] not in self.nodes:
												a_						:						List[str] 							= RadixNode(prefix=_lowercase  ,      is_leaf=_lowercase    )

									else:
												a_						:						Optional[Any] 							= self.nodes[word[0]]
												a_							,					a_							,					a_						:						Optional[Any] 							= incoming_node.match(
												    _lowercase    )

												# Case 3: The node prefix is equal to the matching
												# Solution: We insert remaining word on the next node
												if remaining_prefix == "":
															self.nodes[matching_string[0]].insert(_lowercase    )

												# Case 4: The word is greater equal to the matching
												# Solution: Create a node in between both nodes, change
												# prefixes and add the new node for the remaining word
												else:
															a_						:						List[Any] 							= remaining_prefix

															a_						:						List[Any] 							= self.nodes[matching_string[0]]
															a_						:						Optional[int] 							= RadixNode(_lowercase  ,      _lowercase    )
															a_						:						Tuple 							= aux_node

															if remaining_word == "":
																		a_						:						Dict 							= True
															else:
																		self.nodes[matching_string[0]].insert(_lowercase    )





						def 			UpperCamelCase__					(    self  ,      _lowercase    )     -> bool:
									a_						:						Any 							= self.nodes.get(word[0]  ,      _lowercase    )
									if not incoming_node:
												return False
									else:
												a_							,					a_							,					a_						:						List[Any] 							= incoming_node.match(
												    _lowercase    )
												# If there is remaining prefix, the word can't be on the tree
												if remaining_prefix != "":
															return False
												# This applies when the word and the prefix are equal
												elif remaining_word == "":
															return incoming_node.is_leaf
												# We have word remaining so we check the next node
												else:
															return incoming_node.find(_lowercase    )





						def 			UpperCamelCase__					(    self  ,      _lowercase    )     -> bool:
									a_						:						List[str] 							= self.nodes.get(word[0]  ,      _lowercase    )
									if not incoming_node:
												return False
									else:
												a_							,					a_							,					a_						:						Union[str, Any] 							= incoming_node.match(
												    _lowercase    )
												# If there is remaining prefix, the word can't be on the tree
												if remaining_prefix != "":
															return False
												# We have word remaining so we check the next node
												elif remaining_word != "":
															return incoming_node.delete(_lowercase    )
												else:
															# If it is not a leaf, we don't have to delete
															if not incoming_node.is_leaf:
																		return False
															else:
																		# We delete the nodes if no edges go from it
																		if len(incoming_node.nodes    ) == 0:
																					del self.nodes[word[0]]
																					# We merge the current node with its only child
																					if len(self.nodes    ) == 1 and not self.is_leaf:
																								a_						:						Any 							= list(self.nodes.values()    )[0]
																								a_						:						Optional[int] 							= merging_node.is_leaf
																								self.prefix += merging_node.prefix
																								a_						:						Tuple 							= merging_node.nodes
                    # If there is more than 1 edge, we just mark it as non-leaf
																		elif len(incoming_node.nodes    ) > 1:
																					a_						:						Optional[Any] 							= False
																		# If there is 1 edge, we merge it with its child
																		else:
																					a_						:						Union[str, Any] 							= list(incoming_node.nodes.values()    )[0]
																					a_						:						Any 							= merging_node.is_leaf
																					incoming_node.prefix += merging_node.prefix
																					a_						:						str 							= merging_node.nodes

																		return True





						def 			UpperCamelCase__					(    self  ,      _lowercase = 0    )     -> None:
									if self.prefix != "":
												print("""-""" * height  ,      self.prefix  ,      """  (leaf)""" if self.is_leaf else """"""    )

									for value in self.nodes.values():
												value.print_tree(height + 1    )







def 					_UpperCAmelCase				(						):

			'''simple docstring'''



			a_						:						Union[str, Any] 							= """banana bananas bandana band apple all beast""".split()
			a_						:						Optional[Any] 							= RadixNode()
			root.insert_many(a__)

			assert all(root.find(a__) for word in words)
			assert not root.find("""bandanas""")
			assert not root.find("""apps""")
			root.delete("""all""")
			assert not root.find("""all""")
			root.delete("""banana""")
			assert not root.find("""banana""")
			assert root.find("""bananas""")

			return True


def 					_UpperCAmelCase				(						):

			'''simple docstring'''



			assert test_trie()


def 					_UpperCAmelCase				(						):

			'''simple docstring'''



			a_						:						Optional[int] 							= RadixNode()
			a_						:						List[Any] 							= """banana bananas bandanas bandana band apple all beast""".split()
			root.insert_many(a__)

			print("""Words:"""  ,	a__)
			print("""Tree:""")
			root.print_tree()


if __name__ == "__main__":
	main()





def 					_UpperCAmelCase				(						a__  ,	a__):

			'''simple docstring'''



			return x if y == 0 else greatest_common_divisor(a__  ,	x % y)


def 					_UpperCAmelCase				(						a__  ,	a__):

			'''simple docstring'''



			return (x * y) // greatest_common_divisor(a__  ,	a__)


def 					_UpperCAmelCase				(						a__ = 2_0):

			'''simple docstring'''



			a_						:						Any 							= 1
			for i in range(1  ,	n + 1):
						a_						:						Tuple 							= lcm(a__  ,	a__)
			return g


if __name__ == "__main__":
	print(F"""{solution() = }""")


